Abstract

We introduce a new iterative sequence for finding a
common element of the set of fixed points of a relatively nonexpansive mapping
and the set of solutions of an equilibrium problem in a Banach space. Then, we
study the strong convergence of the sequences. With an appropriate setting, we
obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.